Remarks on a Finsler-Laplacian

Ferone, Vincenzo; Kawohl, Bernd

doi:10.1090/S0002-9939-08-09554-3

Remarks on a Finsler-Laplacian
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by Vincenzo Ferone and Bernd Kawohl PDF

Proc. Amer. Math. Soc. 137 (2009), 247-253 Request permission

Abstract:

We investigate elementary properties of a Finsler-Laplacian operator $Q$ that is associated with functionals containing $(H(\nabla u))^2$. Here $H$ is convex and homogeneous of degree 1, and its polar $H^o$ represents a Finsler metric on $\mathbb R^n$. In particular we study the Dirichlet problem $-Qu=2n$ on a ball $K^o=\{x\in \mathbb R^n : H^o(x)<1\}$ and present a fundamental solution for $Q$, suitable maximum and comparison principles, and a mean value property for solutions of $Qu=0$.

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